A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids

Yongbin Ge, Fujun Cao, Jun Zhang

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a multigrid method is developed to solve the linear system arising from this HOC difference scheme and the corresponding multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.

Original languageEnglish
Pages (from-to)199-216
Number of pages18
JournalJournal of Computational Physics
Volume234
Issue number1
DOIs
StatePublished - 2013

Bibliographical note

Funding Information:
This work is supported by the National Natural Science Foundation of China under Grants 11061025 and 11161036 , the Key Project of China Ministry of Education under Grant 210239 , and the Fok Ying-Tong Education Foundation of China under Grant 121105 .

Keywords

  • Hoc scheme
  • Multigrid method
  • Nonuniform grids
  • Poisson equations
  • Volume law

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy (all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids'. Together they form a unique fingerprint.

Cite this